Scanning tunneling microscopy and spectroscopy of graphene layers on graphite

We report low temperature scanning tunneling microscopy and spectroscopy on graphene flakes supported on a graphite substrate. The experiments demonstrate that graphite is exceptionally well suited as a substrate for graphene because it offers support without disturbing the intrinsic properties of the charge carriers. The degree of coupling of a graphene flake to the substrate was recognized and characterized from the appearance of an anomalous Landau level sequence in the presence of a perpendicular magnetic field. By following the evolution of the Landau level spectra along the surface, we identified graphene flakes that are decoupled or very weakly coupled to the substrate. From the Landau level sequence in this flake, we extract the local Fermi velocity and energy of the Dirac point and find extremely weak spatial variation of these quantities confirming the high quality and non invasive nature of the graphite substrate.     

The ν1 and ν4 fundamental bands of H3SiCl investigated with high resolution

The gas phase infrared spectrum of monoisotopic H₃Si³⁷Cl has been reinvestigated in the ν₁/ν₄ region near 2200 cm⁻¹, using a Fourier transform spectrometer, with a nominal resolution of 0.0027 cm⁻¹. The rovibrational analysis confirms, besides the weak Coriolis x, y resonance between the (v₁ = 1) and (v₄ = 1) levels, the existence of two strong local perturbations in the ν₄ band. These are caused by rotational (Δk = Δl = ±1) type resonances with and , respectively. Another local perturbation of the 12 ? KΔK ? 14 subbands of the ν₄ band, probably due to a (Δk = Δl = ±1) interaction with , was detected and analyzed. All these local perturbations have been studied individually using a simple model of two interacting sublevels. Without the transitions involved in the local perturbations, more than 2000 lines of the ν₁/ν₄ band system were used to obtain a complete set of vibration-rotation parameters set for the v₁ = 1 and v₄ = 1 states. By means of a band contour simulation, both the transition moment ratio ∣M₄:M₁∣ = 1.25 and a positive sign of the Coriolis intensity perturbation were determined.The present results, together with the accurate existing data for ν₂, ν₃, ν₅, and ν₆ bands, allowed us to derive the experimental values, A_e = 2.8722945(37) cm⁻¹ and B_e = 0.2182248(22) cm⁻¹, which are compared with those of ab initio calculations.     

Rovibrational spectroscopy of the Fermi-interacting ν4 = 1 and ν3 = ν6 = 1 levels of DCF3

The high-resolution infrared spectrum of deuterated fluoroform (DCF₃) was studied in the 700 and 1200 cm⁻¹ regions, with the aim of assigning and analyzing the ν₄ CF₃ asymmetric stretching vibration. The Fermi-type anharmonic coupling between the ν₄ = 1 and ν₃ = ν₆ = 1 rovibrational levels, already mentioned in an early work of Ruoff et al. [Spectrochimica Acta Part A 31A (1975) 1099-1100], was studied here for the first time under high resolution. Assignments in the ν₃ + ν₆/ν₄ band system were confirmed and extended by the identification of the ν₃ + ν₆ − ν₆ and ν₄-ν₆ bands in the 700 cm⁻¹ region, the latter being enhanced near the Fermi crossings of the studied levels. Data from both the hot and difference bands were included in the analysis. The close separation of the studied vibrational levels of about 14.8 cm⁻¹ produces a large variety of resonance crossings which involve levels with . Besides the Fermi () and Coriolis () resonances, they were accounted for by inclusion of additional higher-order ( and ) interaction terms between the vibrational states. The least-squares fit of more that 16,000 vibration-rotation transitions provides a quantitative reproduction of data in all bands.     

Integral Equations, Dichotomy of Evolution Families on the Half-Line and Applications

The purpose of this paper is to provide a new, unified and complete study for uniform dichotomy and exponential dichotomy on the half-line. First we deduce conditions for the existence of uniform dichotomy, using classes of function spaces over _+{\mathbb {R}_+} which are invariant under translations. After that, we obtain a classification of the main classes of function spaces over \mathbb R₊{\mathbb {R}_+}, in order to deduce necessary and sufficient conditions for the existence of exponential dichotomy, emphasizing on the main technical qualitative properties of the underlying spaces. We motivate our approach by illustrative examples and show that the main hypotheses cannot be dropped. We provide optimal methods regarding the input space in the study of dichotomy and deduce as particular cases some interesting situations as well as several dichotomy results published in the past few years.     

Polyethylene glycol as a non-ionic liquid solvent for polyoxometalate catalyzed aerobic oxidation

The H5PV2Mo10O40 polyoxometalate in a polyethylene glycol solvent was effective for a series of aerobic oxidation reactions including oxydehydrogenation of alcohols and cyclic dienes, oxidation of sulfides and the Wacker reaction; the solvent-catalyst phase can be recovered and recycled.     

Light Energy Collection in a Porphyrin–Imide–Corrole Ensemble

An assembly consisting of three units, that is, a meso‐substituted corrole ( C3 ), 1,8 naphthaleneimide ( NIE ), and a Zn porphyrin ( ZnP ), has been synthesized. NIE is connected to C3 through a 1,3‐phenylene bridge and to the ZnP unit through a direct C? C bond. The convergent synthetic strategy includes the preparation of a trans‐A₂B‐corrole possessing the imide unit, followed by Sonogashira coupling with a meso‐substituted A₃B‐porphyrin. The photophysical processes in the resulting triad ZnP-NIE-C3 are examined and compared with those of the corresponding C3-NIE dyad and the constituent reference models C3 , NIE , and ZnP . Excitation of the NIE unit in C3-NIE leads to a fast energy transfer of 98 % efficiency to C3 with a rate k_en=7.5×10¹⁰ s^?1, whereas excitation of the corrole unit leads to a reactivity of the excited state identical to that of the model C3 , with a deactivation rate to the ground state k=2.5×10⁸ s^?1. Energy transfer to C3 and to ZnP moieties follows excitation of NIE in the triad ZnP-NIE-C3 . The rates are k_en=7.5×10¹⁰ s^?1 and k_en=2.5×10¹⁰ s^?1 for the sensitization of the C3 and ZnP unit, respectively. The light energy transferred from NIE to Zn porphyrin unit is ultimately funneled to the corrole component, which is the final recipient of the excitation energy absorbed by the different components of the array. The latter process occurs with a rate k_en=3.4×10⁹ s^?1 and 89 % efficiency. Energy transfer processes take place in all cases by a Förster (dipole–dipole) mechanism. The theory predicts quite satisfactorily the rate for the ZnP/C3 couple, where components are separated by about 23 Å, but results in calculated rates that are one to two orders of magnitude higher for the couples NIE/ZnP (D/A) and NIE/C3, which are separated by distances of about 14 and 10 Å, respectively.     

Solid Lipid Nanoparticles (SLNs): Preparation and Properties of Calix[4]resorcinarene Derived Systems.

Solid Lipid Nanoparticles (SLNs) have been prepared fromc-2,c-8,c-14,c-20-tetraundecyl-4,6,10,12,16,18,22,24-octahydroxyresorc[4]areneas colloidal suspensions. Photon Correlation Spectroscopy studies revealed aparticle hydrodynamic diameter of 150 nm. Non-contact mode Atomic ForceMicroscopy allows observation of the particles as slightly flattened sphericalobjects of 236 (±40) nm diameter and 145 (±40) nm height. Thestudy of the preparation parameters showed that shear force does not affectthe hydrodynamic size of the SLNs. In contrast, the viscosity and the pH ofthe aqueous phase, the amphiphile concentration in the organic phase and thevolume of organic phase used, all lead to variation in the size of the particles.In term of post preparation parameters only the ionic strength has been shownto affect significantly the particle size; while the pH of the storing solution,microwave, ultrasonic and thermal treatments do not. Short and long-termstability studies have been performed to measure the effect of the ionic strengthon the stability of the particles. The use of carbohydrate cryoprotectants does notallow re-dispersion of the colloidal suspension after freeze-drying.     

An H2-Type Norm of a Discrete-Time Linear Stochastic System with Periodic Coefficients Simultaneously Affected by an Infinite Markov Chain and Multiplicative White Noise Perturbations

This article investigates the problem of the definition and computation of an H₂-type norm for discrete-time time-varying periodic stochastic linear systems simultaneously affected by multiplicative white noise perturbations and random jumping according to a Markov chain with an infinite countable number of states. Also, we solve an optimization problem that contains, as a special case, the H₂ optimal control problem for the considered class of stochastic systems under the assumption of perfect state measurements.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations

In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem (or cell problem), i.e. we construct solutions of the form $\lambda t + v(x).$ We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (1) the fact that we handle the case of “mixed operators” for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (2) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.